Use definition to find derivative of the following function at $z = 3 - 2 i$
$f (z) = 3^{2} - 2 i z + 6$

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Use definition to find derivative of the following function at z=3−2if(z)=32−2iz+6

bondsk384r · Accepted Answer

Step 1&amp;nbsp;Given,function&amp;nbsp;f(z)=322-2iz+6Step 2for first derivative using defination of limitf′(z)=lim△z→0f(z+△z)−f(z)△zNow put&amp;nbsp;z→z+△z⇒f′(z)=lim△z→03(2+△z)2−2i(z+△z)+6△z⇒lim△z→03(z2+2×2×△z+(△z)2)−2iz−2i△z+6△z⇒lim△z→03z2+6×z×△z+3(△z)2−2iz−2i△z+6△z⇒lim△z→03z2+6×2×△z+3(△z)2−2iz−2i△z+6}{△z}⇒lim△z→03z2−2iz+6△z+3(△z)2+6×z×△z−2i△z△z⇒lim∆z→03z2-2iz+6∆z+(∆z)(3∆z+6z-2i)(∆z)Put&amp;nbsp;△z→0⇒3z2−2i(0)+60+(3×0+6z−2i)⇒0+6z-2i⇒f′(z)=6z−2iStep 3Now value of derivate&amp;nbsp;z=3−2if′(3−2i)=6(3−2i)−2i=18−12i−2i=18−14iHence, derivative of following function at&amp;nbsp;z=3-2i&amp;nbsp;is&amp;nbsp;18-14i

Use definition to find derivative of the following

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